Etendue⚠ unverified
Physics / Optics · Compute the etendue (throughput) of an optical system
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| A | A | m**2 | 1.0 | Area of the aperture or source |
| Omega | Ω | sr | 1.0 | Solid angle subtended |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | G | m**2 * sr | Etendue, in square metre steradians (m**2 * sr) |
The science & history
Understanding the Parameters
- $A$, $\Omega$ — larger source or wider cone → larger etendue.
- $G$ — full definition often includes $n^{2}$ ($G = n^{2} A\Omega$); this card is the $n=1$ geometric product.
Derivation (Approaching a Proof)
Phase-space volume of rays: area × solid angle (and $n^{2}$ in a medium). Liouville’s theorem / brightness theorem ⇒ etendue cannot decrease in passive optics.
History
Etendue (throughput, AΩ product) is fundamental in nonimaging optics and illumination design.
Related Concepts: Numerical Aperture, Optical Path Length, Lens Power
Notes: Registry calculator etendue (unverified). Geometric $A\Omega$ only (no $n^{2}$).